.At what rate, in stere per minute, is the volume of a sphere increasing if the radius of the sphere is three

Question

...meters in length and is increasing at a rate of three meters per minute.

Stere: a cubic meter equivalent to 35.315 cubic feet or 1.3080 cubic yards, used to measure cordwood.

Answer 1

V = (4/3)*π*r^3

dV/dt = 4π*r^2 (dr/dt)

Since r = 3 m and dr/dt = 3 m/min, we have

dV/dt = 4π(9)(3) ≈ 339.292 m^3/min = 339.292 stere/min.

Answer 2

Righty,

dr/dt = 3 m/min (rate of change of radius r)
r = 3 m (radius)
V=4/3.pi.r^3 (volume in terms of radius for a sphere)
dV/dr = 4.pi.r^2 (rate of change of volume with respect to the radius - differential of above line)

We want rate of change of volume per minute, i.e.
dV/dt
which = dr/dt * dV/dr (since differentials act like fractions)
= 3 * 4.pi.r^2
= 12.pi.r^2

So if r=3 volume's rate of change is 108.pi m^3/min (steres)
which is about 339.292
Is that useful? I might have made a mistake but I can't see where if I have.